Problem: When a number is divided by 7, the remainder is 2. What is the remainder when three times the number minus 7 is divided by 7?
Explanation: If our number is $n$, then $n \equiv 2 \pmod 7$.  This tells us that  \[3n - 7 = n + n + n - 7 \equiv 6 - 0 \pmod 7.\]The remainder is $\boxed{6}$ when the number is divided by $7.$